Synchronisation by noise for the stochastic quantisation equation in dimensions $2$ and $3$

Abstract

We prove uniform synchronisation by noise with rates for the stochastic quantisation equation in dimensions two and three. The proof relies on a combination of coming down from infinity estimates and the framework of order-preserving Markov semigroups derived in [Butkovsky, Scheutzow; 2019]. In particular, it is shown that this framework can be applied to the case of state spaces given in terms of Hölder spaces of negative exponent.

arXiv comment13 pages

References in corpus (4)

• Random attractors for degenerate stochastic partial differential equations
• Couplings via comparison principle and exponential ergodicity of SPDEs in the hypoelliptic setting
• The support of singular stochastic PDEs
• Ergodicity for Stochastic Porous Media Equations